OFFSET
1,1
COMMENTS
This sequence is infinite and its relative density in the sequence of primes is 1 - Product_{p prime} (1-1/(p^2*(p-1))) = 1 - A065414 = 0.30249864150363409671... (Jakimczuk, 2024). - Amiram Eldar, Jul 20 2024
LINKS
Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Rafael Jakimczuk, Numbers of the form p-1 where p is prime, ResearchGate preprint, 2024.
MATHEMATICA
f[n_]:=Max[Last/@FactorInteger[n]]; lst={}; Do[p=Prime[n]; If[f[p-1]>=3, AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 03 2009 *)
Select[Prime[Range[200]], Count[Transpose[FactorInteger[#-1]][[2]], _?(#>2&)]>0&] (* Harvey P. Dale, Jan 01 2012 *)
PROG
(PARI) ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) }
powerfreep3(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(ispowerfree(x+k, p)==0, c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) }
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Dec 08 2003
STATUS
approved